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How many even numbers less than 10000 can be formed by using the digits 2, 4, 3, and 5 if repetition of the digits is allowed?

A. 32
B. 16
C. 44
D. 41

Answer :

Final answer:

To calculate the even numbers less than 10000 formed with 2, 4, 3, and 5, we use the counting principle on each digit place, resulting in 96 possible even numbers.

Explanation:

To find out how many even numbers less than 10000 can be formed using the digits 2, 4, 3, and 5 with repetition allowed, we need to consider the place values. An even number must end in an even digit, thus either a 2 or a 4. Counting from right to left, the units place (first position) can be filled by 2 options (2 or 4), the tens place (second position) by 4 options (since it can be any of the four given digits), the hundreds place (third position) similarly by 4 options, and the thousands place (fourth position) by 3 options (since it can only be 2, 3, or 4 to ensure the number is less than 10000).

Using the counting principle, we multiply the number of options for each position: 3 × 4 × 4 × 2 = 96. There are 96 possible even numbers less than 10000 that can be formed with the digits 2, 4, 3, and 5 when repetition of digits is allowed.

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